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Solve for x and write your answer in simplest form. -(3)/(2)+x=-(-(1)/(5)x-(1)/(2))-x Answer: x=

Solve for x x and write your answer in simplest form.\newline−32+x=−(−15x−12)−x -\frac{3}{2}+x=-\left(-\frac{1}{5} x-\frac{1}{2}\right)-x \newlineAnswer: x= x=

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Q. Solve for x x and write your answer in simplest form.\newline−32+x=−(−15x−12)−x -\frac{3}{2}+x=-\left(-\frac{1}{5} x-\frac{1}{2}\right)-x \newlineAnswer: x= x=
  1. Write Given Equation: Write down the given equation.\newlineThe given equation is: −32+x=−(−15x−12)−x-\frac{3}{2} + x = -\left(-\frac{1}{5}x - \frac{1}{2}\right) - x
  2. Simplify Right Side: Simplify the right side of the equation.\newlineTo simplify the right side, we need to distribute the negative sign across the terms inside the parentheses.\newline−(−15x−12)-\left(-\frac{1}{5}x - \frac{1}{2}\right) becomes 15x+12\frac{1}{5}x + \frac{1}{2}\newlineSo the equation now is: −32+x=15x+12−x-\frac{3}{2} + x = \frac{1}{5}x + \frac{1}{2} - x
  3. Combine Like Terms: Combine like terms.\newlineWe have xx on both sides of the equation, so we will combine them.\newlineTo do this, we add xx to both sides to get all xx terms on one side.\newline−32+x+x=15x+12−x+x-\frac{3}{2} + x + x = \frac{1}{5}x + \frac{1}{2} - x + x\newlineThis simplifies to: −32+2x=15x+12-\frac{3}{2} + 2x = \frac{1}{5}x + \frac{1}{2}
  4. Subtract Terms: Subtract 15x\frac{1}{5}x from both sides to get all xx terms on one side.\newline−32+2x−15x=15x+12−15x-\frac{3}{2} + 2x - \frac{1}{5}x = \frac{1}{5}x + \frac{1}{2} - \frac{1}{5}x\newlineThis simplifies to: −32+105x−15x=12-\frac{3}{2} + \frac{10}{5}x - \frac{1}{5}x = \frac{1}{2}
  5. Combine X Terms: Combine the xx terms on the left side.(105)x−(15)x=(95)x\left(\frac{10}{5}\right)x - \left(\frac{1}{5}\right)x = \left(\frac{9}{5}\right)x So the equation now is: −32+95x=12-\frac{3}{2} + \frac{9}{5}x = \frac{1}{2}
  6. Add to Isolate X Term: Add (32)(\frac{3}{2}) to both sides to isolate the x term.\newline−32+95x+32=12+32-\frac{3}{2} + \frac{9}{5}x + \frac{3}{2} = \frac{1}{2} + \frac{3}{2}\newlineThis simplifies to: 95x=42\frac{9}{5}x = \frac{4}{2}
  7. Simplify Right Side: Simplify the right side of the equation.\newline(4)/(2)(4)/(2) simplifies to 22.\newlineSo the equation now is: (9/5)x=2(9/5)x = 2
  8. Solve for X: Solve for xx by dividing both sides by (9/5)(9/5).\newlineTo isolate xx, we divide both sides by (9/5)(9/5), which is the same as multiplying by the reciprocal, (5/9)(5/9).\newlinex=2×(5/9)x = 2 \times (5/9)
  9. Multiply to Find X: Multiply to find the value of xx.x=2×(59)x = 2 \times \left(\frac{5}{9}\right)x=(2×5)/9x = \left(2 \times 5\right) / 9x=109x = \frac{10}{9}

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